Problem: There is a light source on the plane. This source is so small that it can be represented as point. The light source is moving from point (a, s_y) to the (b, s_y) (s_y < 0) with speed equal to 1 unit per second. The trajectory of this light source is a straight segment connecting these two points. 

There is also a fence on OX axis represented as n segments (l_i, r_i) (so the actual coordinates of endpoints of each segment are (l_i, 0) and (r_i, 0)). The point (x, y) is in the shade if segment connecting (x,y) and the current position of the light source intersects or touches with any segment of the fence.

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You are given q points. For each point calculate total time of this point being in the shade, while the light source is moving from (a, s_y) to the (b, s_y).

Input

First line contains three space separated integers s_y, a and b (-10^9 ≤ s_y < 0, 1 ≤ a < b ≤ 10^9) — corresponding coordinates of the light source.

Second line contains single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — number of segments in the fence.

Next n lines contain two integers per line: l_i and r_i (1 ≤ l_i < r_i ≤ 10^9, r_{i - 1} < l_i) — segments in the fence in increasing order. Segments don't intersect or touch each other.

Next line contains single integer q (1 ≤ q ≤ 2 ⋅ 10^5) — number of points to check.

Next q lines contain two integers per line: x_i and y_i (1 ≤ x_i, y_i ≤ 10^9) — points to process.

Output

Print q lines. The i-th line should contain one real number — total time of the i-th point being in the shade, while the light source is moving from (a, s_y) to the (b, s_y). The answer is considered as correct if its absolute of relative error doesn't exceed 10^{-6}.

Example

Input

-3 1 6
2
2 4
6 7
5
3 1
1 3
6 1
6 4
7 6


Output

5.000000000000000
3.000000000000000
0.000000000000000
1.500000000000000
2.000000000000000

Note

  * The 1-st point is always in the shade; 
  * the 2-nd point is in the shade while light source is moving from (3, -3) to (6, -3); 
  * the 3-rd point is in the shade while light source is at point (6, -3). 
  * the 4-th point is in the shade while light source is moving from (1, -3) to (2.5, -3) and at point (6, -3); 
  * the 5-th point is in the shade while light source is moving from (1, -3) to (2.5, -3) and from (5.5, -3) to (6, -3); 

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Vadim Semenov
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static final class TaskE {
        private long[][] segments;
        private long[] sum;

        public void solve(int __, InputReader in, PrintWriter out) {
            long y0 = in.nextInt();
            long a = in.nextInt();
            long b = in.nextInt();
            int segmentsQty = in.nextInt();
            segments = new long[segmentsQty + 1][2];
            for (int i = 1; i <= segmentsQty; ++i) {
                for (int j = 0; j < 2; ++j) {
                    segments[i][j] = in.nextInt();
                }
            }
            sum = new long[segmentsQty + 1];
            for (int i = 1; i <= segmentsQty; ++i) {
                sum[i] = sum[i - 1] + segments[i][1] - segments[i][0];
            }
            int qty = in.nextInt();
            for (int i = 0; i < qty; ++i) {
                int x = in.nextInt();
                int y = in.nextInt();
                long yy = y - y0;
                long xa = a * y - x * y0;
                long xb = b * y - x * y0;
                long shadeSize = getShadeSize(xb, yy) - getShadeSize(xa, yy);
                out.printf("%.15f\n", (double) shadeSize * (b - a) / (xb - xa));
            }
        }

        private long getShadeSize(long x, long div) {
            int ptr = 0;
            int upper = segments.length;
            while (upper - ptr > 1) {
                int mid = (ptr + upper) >>> 1;
                if (segments[mid][0] * div <= x) {
                    ptr = mid;
                } else {
                    upper = mid;
                }
            }
            long shade = 0;
            if (segments[ptr][1] * div > x) {
                shade += x - segments[ptr][0] * div;
                ptr--;
            }
            return shade + sum[ptr] * div;
        }

    }

    static class InputReader {
        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(readLine());
            }
            return tokenizer.nextToken();
        }

        public String readLine() {
            String line;
            try {
                line = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }

    }
}